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A simple proof of the generalized Cauchy’s theorem. (English) Zbl 1331.74021

Summary: Cauchy’s theorem for balance laws is proved in a general context using a simpler and more natural method in comparison to the one recently presented in [R. Segev, Arch. Ration. Mech. Anal. 154, No. 3, 183–198 (2000; Zbl 0965.58004)]. By “generality” we mean that the ambient space is considered to be an orientable smooth manifold, and not only the Euclidean space.

MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids

Citations:

Zbl 0965.58004
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References:

[1] Segev, R.: The geometry of Cauchy’s fluxes. Arch. Ration. Mech. Anal. 154, 183–198 (2000) · Zbl 0965.58004 · doi:10.1007/s002050000089
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[3] Aubram, D.: Differential Geometry Applied to Continuum Mechanics. Shaker, Aachen (2009)
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[6] Lee, J.M.: Introduction to Smooth Manifolds. Springer, New York (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.